tag:blogger.com,1999:blog-26410089.post1706434658792166922..comments2022-12-07T22:51:11.903-08:00Comments on hagiograffiti: Science Has No Use For Ockham's RazorManuel Moertelmaierhttp://www.blogger.com/profile/00311854798880262444noreply@blogger.comBlogger3125tag:blogger.com,1999:blog-26410089.post-39693095752273364892010-07-10T05:56:59.705-07:002010-07-10T05:56:59.705-07:00We can use Solomonoff in certain special cases suc...We can use Solomonoff in certain special cases such as where the disparity is HUGE (God vs. gravity) or where we have one theory included in another.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-26410089.post-11274261981592677782008-05-25T11:38:00.000-07:002008-05-25T11:38:00.000-07:00Well, there's a indeed a point to that. If we *cou...Well, there's a indeed a point to that. If we *could* use Solomonoff Induction in everyday situations, Occam's Razor would indeed declare itself to be superfluous "explanation" of sorts (Compare EURISKOs famed "it's a good idea to throw out a randomly chosen heuristic" heuristic, which by chance was applied first (and last) to itself, or my ad-hoc-invented "Schmirgelberger's Razor" which states that "Generic rules pulled out of thin air are generally bullshit, this being especially true for Schmirgelberger's Razor", etc) <BR/><BR/>But in reality Solomonoff induction, though theoretically optimal, is absolutely impractical in everyday reasoning. One could argue that Occam's Razor embodies something akin to the MDL (MML) principle applied to an extremely complex description language (the "language of human thought", in poetic terms.) The ecological validity of the MDL principle can be argued to stem from the optimality of Solomonoff induction, plus the, again poetic, statement that "evolution did a good job on us." We're treading on really thin ice here, and have long left the ground of mathematically justifiable statements. In fact, I cannot give a stringent reason why Occam's Razor is useful. I can't even provide any hard evidence that it *is* in fact useful. Maybe slightly more complex explanations are better suited to be processed by (human) neural networks, or maybe they lead to new creative insights more quickly etc. I simply don't know. Occam's Razor is, and that is my big point in this post, a piece of armchair reasoning, and nothing more, due to the impossibility of rigorously defining what is "simple" in terms of human "explanations". It's justifiable to use the MDL principle in mathematical data analysis, but if you're talking about who murdered Lady Abigail at midnight, you shalt not invoke the name of Solomonoff. <BR/><BR/>So if Solomonoff Induction can't explain why Occam's Razor works (does it?), how about the other way round ? This idea can be quickly discarded. Solomonoff equals Bayes plus the assumption that our input from the world is produced by a computable process. Nothing more here, no initial preference for simplicity at all. Solomonoff induction could very well be invented by a mathematically competent civilization that has never produced any figure like Occam, even if, admittedly, Occam's work may have been an inspiration to Ray Solomonoff in our world. <BR/><BR/>Besides, I'm not feeling too comfortable with the term "works" here, as Solomonoff induction is in fact incomputable. It's more like the north star - it tells you in which direction to go, but you shouldn't think you can actually reach it.Manuel Moertelmaierhttps://www.blogger.com/profile/00311854798880262444noreply@blogger.comtag:blogger.com,1999:blog-26410089.post-14070908650862066392008-05-24T16:18:00.000-07:002008-05-24T16:18:00.000-07:00So, you're saying, by Occam's Razor, we have to re...So, you're saying, by Occam's Razor, we have to remove Occam's Razor from our explanation for why Solomonoff induction works? ;-)Anonymousnoreply@blogger.com